External current drive (CD) is an important prerequisite for the control of the plasma current profile in advanced tokamak scenarios as well as for the development of quasi-stationary, fully noninductivly driven tokamak discharges. On ASDEX Upgrade, three heating systems, neutral beam injection, ion cyclotron resonance heating, and electron cyclotron resonance heating, are available for this purpose. The status of CD modeling and the CD capability of these systems are reviewed, and a brief overview is provided of what has been achieved experimentally with respect to CD in various discharge scenarios.